Existence conjecture for lens space knots in Brieskorn homology spheres

Let $\Sigma(p,q,r)$ be a Brieskorn homology sphere, and let $K_{p,k}$ denote a parameterized lens space knot. Existence conjecture. Every Brieskorn homology sphere contains a knot $K_{p,k}$. The source explains that the tables constructed there do not cover all Brieskorn homology spheres, giving $\Sigma(7,11,15)$ as an example whose status is undetermined; this conjecture is therefore open.